Wet adiabat and speed of sound in cloud

[chornedsnorkack]

Clouds have much lower adiabatic gradient than dry or moist air that contains free water. This is because free water absorbs latent heat of evaporation on adiabatic compression.

The speed of sound is determined by adiabatic compressibility. Newton got the speed of sound about 20 % too slow because he tried to compute it from isothermal compressibility.

Shouldnīt the speed of sound then be far slower in clouds than in clear air?

[Rainboe]

zzzzzzzzzzzzzzzzzzz

[ft]

Going outside of my area of expertise (in other words, speculating), I'd say no.

The adiabat is changed due to water evaporating as the temperature increases with pressure increases, thus reducing the temperature change. Heat transfer from air to water = not an adiabatic process.

With the pressure changes associated with sound waves propagating through the air, the water droplets will not have time to evaporate and condensate to any significant degree with the small pressure variations caused by the sound waves. In other words, (dry) adiabatic compression.

If the air had time to transfer heat to the water droplets, you would in fact be leaving the adiabatic process behind as heat transfer from the medium (air) into a reservoir (the water) would take place. As you point out, you'd be getting closer to the isothermal process assumed by Newton.

Makes sense? If not, I blame it on management!

Rgds,
/Fred

[Yay!!!]

I think it's all about the air pressure.
The speed of sound increases when there is less air
and decreases when there is more

[enicalyth]

omigod!

Back to school the lot of you except rainboe and stay in class. Try this website of Richard Shelquist's Calculator Index Page and don't ask questions until you a) understand what is meant by perfect gas behaviour b) understand that air including moisture vapour very closely resembles a perfect gas c) understand that water droplets are liquid. Oh my Lordy. And for adiabatic compressibility of air and kerosene droplets including flame temperature and local speed of sound try mechanics and thermodynamics of propulsion by Philip Hill and Carl Peterson. I don't think the kerosene droplets compress by much do you?

[john_tullamarine]

The equations are of similar form whether for dry or moist air, moist air being less dense and introducing a variation to gamma.

Typically, the effect of water vapour on sonic velocity is something like

a*sqrt(gamma/(1.4(1-0.3783(partial vapour pressure/static pressure))))

NACA-TR-919 is a fairly standard sort of reference and suggests that, for airspeed calculations, the humidity effect on airspeed measurement is within the range 0.4 - 1.4 percent (increasing with temperature) and, in general, not worth worrying about for flight test purposes or, by extension, routine flying operations.

For our pilot-type needs, the idealised equation

a/a0 = sqrt(T/T0)

works fine.

I think it's all about the air pressure

.. sure is .. but you have to include density as well ... so pressure doesn't tell the story by itself

.. and, pardon my ignorance ... what is "adiabat" ?

[parabellum]

I did my licences at a place called Avigation, in Ealing, London and Tommy, the instructor, used to drum into us that the speed of sound was proportional, (or should that be inversely proportional?) to the square root of the absolute temperature, it used to come up in the Nav General exam.
(Sorry Tommy, it was a long time ago!).

[ft]

The simple and often taught answer is that the speed of sound is directly proportional to the square root of temperature.

a = sqrt(gamma*R*T) = sqrt(gamma*R)*sqrt(T)

Generally, the factor sqrt(gamma*R) can safely be assumed constant. It will not be a significant factor in day to day operations. That's close enough to the Absolute Truth for flying aircraft.

However, if the water did indeed have time to condense/evaporate, the sqrt(gamma*R) factor would change and the simple relationship with only temperature would no longer hold true. Hence the original posters question.

J T, 'adiabat' would be a very direct translation from my mother tongue, where the word is (rather questionably, I admit) used to designate the adiabatic lapse rate or, more specifically, the chart depicting the adiabatic lapse rate. Ooops! Sorry about the confusion. I did blame it on management...

And again, this is not my area of expertise. Any corrections of facts are welcome!

[Re-entry]

I think ft has got the explanation exactly right on this.

Chorned, I think you are confusing adiabatic lapse rate with the adiabatic compression involved with the propagation of sound waves.

Newton did not know about the gamma factor, you are right on that though.

Humidity (i.e. gaseous H20) has only a negligible effect on the speed of sound, up to about 0.6%.

Another good formula for speed of sound in knots is 38.94*sqrt(T) where T is absolute temp.

[john_tullamarine]

'adiabat' would be a very direct translation from my mother tongue

thanks for that ... understood now ....

[parabellum]

Why is it that, on a morning of very dense fog, one can stand outside and hear noises from great distances?

[Re-entry]

Probably because fog only forms in light winds so there's very little wind noise.

[chornedsnorkack]

With the pressure changes associated with sound waves propagating through the air, the water droplets will not have time to evaporate and condensate to any significant degree with the small pressure variations caused by the sound waves. In other words, (dry) adiabatic compression.

The chord of a wing is just a few metres. The inlets of engines are just a few metres across at most, and less than that in depth. Yet clouds are commonly seen in low-pressure areas above wing and in engine inlets ahead of fan.

A parcel of air moving at hundreds of m/s past an airframe or into an engine spends just a thousandth or a few thousandths of seconds in the low pressure areas. Yet it is enough time for the moisture to condense.

The latent heat of this condensation must be going somewhere.

[john_tullamarine]

Why is it that, on a morning of very dense fog, one can stand outside and hear noises from great distances?

The observation is misplaced slightly .. the significant factor is not fog, rather the conditions which often predispose to fog .. ie high pressure system .. clear, cold night ... negligible wind ... equals pronounced temperature inversion.

Two points are relevant ..

(a) temperature lapse rate

(b) variation of a0 with temperature

End result is that a sound wave ends up refracting back towards the ground .. rather than refracting towards the vertical.

Simple to see in a sketch .. start with an hemispherical pressure wave .. then consider the refraction due to small a0 variations along the wave ..

[ft]

The chord of a wing is just a few metres. The inlets of engines are just a few metres across at most, and less than that in depth. Yet clouds are commonly seen in low-pressure areas above wing and in engine inlets ahead of fan.

Yet you don't see fog when a sound wave is propagating through the atmosphere under the same conditions. Hence something must be different.

I'd take a look at the relative magnitudes of the pressure changes and the effect on temperatures and heat transfer rates.

[john_tullamarine]

Generally we can treat airflow around the aircraft as approximating an adiabatic process. Temperature follows pressure ... pressure drop gives a temperature drop ... relative humidity increases ... if the dewpoint is achieved we see fogging .. all happens in the blink of an eye.

[chornedsnorkack]

So, consider a plane flying.

Letīs say that the ambient free air pressure is 1000 mbar and temperature 30 Celsius. As the air passes above wing, it expands and cools. Suppose that in dry air, the air pressure above wing is 900 mbar. Due to adiabatic cooling, the temperature should be about 21 Celsius now.

The next day, it is precisely the same 1000 mbar and 30 Celsius... but the air is moister. As the air is expanded above the wing, it cools... and saturates and fog forms. Due to the latent heat, the fog is warmer than 21 degrees - say 24 Celsius.

If 21 degree dry air and 24 degree fog had the same density then the 24 degree fog would have higher pressure. Like, 910 mbar rather than 900 mbar. The pressure difference compared to the 1000 mbar free air is 10 % smaller than in dry air... have you then lost 10 % of available lift to the fog?

[Brian Abraham]

Yet you don't see fog when a sound wave is propagating through the atmosphere under the same conditions. Hence something must be different.

Layman speaking here. Probably because the pressure drop is not sufficient. You will see the "fog" from an explosive detonation if the humidity is sufficient, as the shock wave travels outwards.

[B Fraser]

Probably because fog only forms in light winds so there's very little wind noise.

That's radiation fog. Advection fog can form in a moderate breeze.